Math in Real Life

Learn simple interest concepts and the i = p r t formula with a $1000 investment at 5% for 2 years and a $1000 bond at 6% for four years.

Explore compound interest and its difference from simple interest, and apply the formula to monthly, weekly, daily, and continuous compounding.

Examine annuities by modeling regular retirement contributions and comparing them with lump-sum compound growth. Apply the P-based annuity formula and see how monthly or quarterly deposits grow retirement balances.

Learn to solve for time in compound interest problems using logarithms, with monthly compounding and retirement annuities, applying exponential equations to real-life finance goals.

Apply monthly contributions of 250 dollars to an annuity at 9 percent interest compounded monthly to reach 500,000, solving for time with logarithms; about 31 years.

Explore payment annuities and loans, mastering present value, monthly payments, and amortization to plan withdrawals or loan repayments.

Explore real-world probability with the multiplication rule for independent events, the complement method for at least one success, and the birthday problem: five people yield about 2-3% shared birthdays.

Explore the World Series probability problem and learn to apply the binomial formula and multiplication rule to calculate exact and at-least wins in a best-of-seven series.

Learn probability in a best-of-seven World Series with even teams and independent games. Calculate the chances the series ends in four, five, or six games using combinatorics and independence.

Explore the probability of the World Series ending in six or seven games for evenly matched teams, using binomial combinations and three-of-five analyses, and extend to unequal win chances.

Derive probability formulas for a seven-game World Series, including four, five, six, and seven games, for uneven teams, using binomial coefficients and independence assumptions, and verify the total equals one.

Explore Simpson's paradox and observe how overall admission rates can favor one group while each department favors the other, by breaking data into easy, medium, and advanced departments.

Explore linear growth models that describe how populations and other quantities change over time with a fixed amount per period, using rabbits as a practical example.

Explore exponential growth and decay by multiplying the initial population by one plus the growth rate raised to the power t, and observe asymptotes in decay using a medicine example.

Learn to use logarithms to solve equations with a variable in the exponent, estimating population growth from 1.2 million to about 5 million in roughly 58 years, showing exponential growth.

Explore exponential decay in real life with examples of drug absorption and radioactive decay. Learn how to model remaining amounts using percent-per-hour decay and compute values after hours or days.

Solve exponential decay problems using unit conversions and logarithms, estimate time, and apply to radiocarbon dating and cooling objects, then preview logistic growth in the next lesson.

compare linear and exponential growth, then illustrate logistic growth with carrying capacity and a horizontal asymptote, using a closed-form formula with time, initial population, and rate.

Explore a step-by-step example using an adjusted growth equation with carrying capacity 2.5 million and initial 100,000 to compute the growth rate r from P(5)=165, using natural logarithms.

Explore logistic growth models, estimate carrying capacity of 2.5 million, predict populations at 10 and 25 years, and solve for time to reach two million with logarithms.

Explore how exponential decay estimates fossil ages using carbon-14 dating, leveraging half-life and natural log to solve for age from a remaining percentage.

Explore how temperature follows Newton's law of cooling, using exponential decay to model cooling toward ambient temperature, and learn to determine the cooling constant k from data.

Explore exponential decay and the carbon-14 dating method, using a fossil with 2.41 percent of its original carbon-14 to estimate age via half-life of 5,730 years and decay rate.

Explore the plurality voting method, where the most votes wins without necessarily a majority, and compare it with the board count method and plurality with elimination, highlighting pros and cons.

Analyze the Borda count, a ranking-based point system using ranking ballots, as an alternative to plurality, and compare its pros and cons with instant runoff.

Explain instant runoff, a plurality with elimination voting method where last place is eliminated and votes rerouted to second choices until a majority emerges, illustrated with Alaska, California, Hawaii.

Explore apportionment as the method of dividing a fixed 435 congressional seats among states by population, revealing how Hamilton's, Jefferson's, and Huntington–Hill methods determine electoral votes.

Hamilton's method apportions seats using quotas and a standard divisor, rounds down, and distributes surplus by largest fractional parts, illustrated with a New Jersey six-county example.

Explore Jefferson's method for apportionment, using standard and modified divisors to allocate seats, with a college tutoring example, and compare it to Hamilton's method.

Explore the Huntington-Hill method for apportioning the U.S. House seats, including standard divisor, standard quota, geometric mean, and rounding decisions that reduce paradox risk, with a possible modified divisor.